If and are function and is one-to-one, must f be one-to-one? Prove or give a counterexample.
If are two functions and is one-to-one, then whether must be one-to-one or not.
are two functions.
A function is said to be one-to-one function if distinct elements in domain must be mapped with distinct elements in co-domain.
Let be any sets and the functions are .
The objective is to prove the result, if is one-to-one then must be one-to-one.
To prove the function is one-to-one, it is enough to show that if .
For any in with
As is a function from
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